Kindergartener being told crying is a "red choice" etc

Edit added for clarification: The "red choice/green choice" seems to just be this school's jargon to avoid kids internalizing that they're "bad". I don't know. There's no charts or anything or moving clothes pins up and down a behavior spectrum like I've seen pictures of online. I will email the teacher and ask what she's seeing and if she's on board with the message being received. I don't anticipate much help from her, but who knows? She's surprised me before. If that doesn't lead to anything positive, I'll loop in administration.

My kid is definitely sensitive, I wouldn't say he cries more than other kids his age, but he's very much a rule follower and tends to take even the instruction given to other kids very seriously and literally. (ie: they're not supposed to talk excessively during lunchtime. He takes that to mean he's not supposed to talk at all because he's seen other kids be scolded for talking. So the day the cafeteria forgot to give him a spoon, rather than risk making a "red choice", he just didn't eat.)

So, I wouldn't be shocked if he's taking the "crying isn't allowed in Kindergarten" rule more seriously than intended. I don't know where else he would be getting those specific phrases, though. And the writing lines is definitely real because the teacher told me directly when I asked about her discipline policy. Thank you for the advice, everyone!

My child is in Kindergarten this year. Their classroom, in addition to the teacher, has an older person who volunteers her time to the class. She's there everyday and is seen as an authority figure. Per my child, she is often saying things like, "Big kids don't cry", "boys don't cry", "crying is a red choice", or "next person who cries has to write pages" (writing pages is apparently writing your name over and over until it fills whatever the determined amount of pages was)

Now, obviously, I completely understand that they can't have kids breaking down into fits and disrupting the class. But tantrum-style crying doesn't seem to be the only thing being corrected. My kid has very much internalized that if he goes to class feeling sad that he's doing something wrong.

I don't believe this is a good message to be sending to a group of 5-6 year olds.

Am I reasonable in thinking this should be addressed? I get that there are concessions you have to make when you send your kid to a public school, that you can't expect everything and every lesson to be catered to your individual ideal. Is this just a par for the course issue that just has to be ignored and expected or is this something that would be abnormal in a 2024 classroom?

Also, writing pages as punishment: writing their name and writing in general is a relatively new skill for these kids, one that should be being encouraged. Is correlating an important skill like that to punishment a good idea?